When a medium-sized bottle filled with water quarterly falls from a height with acceleration $g$, the water remains calm. But when it falls with acceleration $>>g$, the water abruptly rises up as if some upward-force were present. Why does the water rise up? And where does the water get the energy from for rising up? I want to know it from both the frames: mine(inertial);falling bottle(non-inertial).
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$\begingroup$ "But when it falls with acceleration >>g" How is this achieved? Is there a more detailed description or a movie on the Internet? $\endgroup$– bright magusDec 10, 2014 at 8:47
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$\begingroup$ @bright magus: Sir,my book describes it as superweightlessness. You can force a water-filled bottle to accelerate it greater than $g$. What happens? The water rises up! $\endgroup$– user36790Dec 10, 2014 at 9:00
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$\begingroup$ I am asking, because in order to give a bottle (with water) acceleration g, you only need to let it go when standing high above the ground, while in order to give is acceleration greater than g, you need to actually give it a push. And this is important. $\endgroup$– bright magusDec 10, 2014 at 9:51
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$\begingroup$ @bright magus: Sir, I have told the same thing in the preceeding comment: you have to give force to make it happen. Actually my book described the phenomenon using man in a lift. When the lift falls with acceleration greater than $g$, man rises up! $\endgroup$– user36790Dec 10, 2014 at 9:58
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$\begingroup$ "When the lift falls with acceleration greater than g, man rises up!" That's obvious because he is still being accelerated only at g by the Earth, so the lift is moving faster. And that's why I asked about the details of the experiment with the bottle. If it is continuously accelerated at >>g (held by hand, etc.), this acceleration is applied to the bottle only, while the water inside is accelerated by the gravitation. Some water will by pushed by bottle's narrowing down and accelerate with it, but some will escape through the mouth and move at g only. So Pranav's answer is generally correct $\endgroup$– bright magusDec 10, 2014 at 10:35
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1 Answer
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The water inside is a fluid, so it isn't rigidly attached to the walls of the bottle. This means that the bulk of the water will still accelerate at $g$, save for the part of the water close to the bottle walls, which will be dragged along with the bottle. The water isn't really rising up, it's just falling slower than the bottle.
In the frame of the falling bottle, you see the water accelerating upwards at $(a_{\rm bottle} - g)$, and the ground accelerating towards you at $a_{\rm bottle}$
In the frame of the water, you see the ground accelerating towards you at $g$ and the bottle accelerating downwards at $a_{\rm bottle} - g$
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$\begingroup$ Can you tell,sir, how can I apply pseudo force with respect to the bottle's non-inertial frame? $\endgroup$– user36790Dec 10, 2014 at 13:03